Power residue symbol information

theory the n-th power residue symbol (for an integer n > 2) is a generalization of the (quadratic) Legendre symbol to n-th powers. These symbols are used in...

(nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is −1. Its value at zero is 0. The Legendre symbol was introduced by...

In mathematics, the Hilbert symbol or norm-residue symbol is a function (–, –) from K× × K× to the group of nth roots of unity in a local field K such...

symbol, a generalization of the Jacobi symbol to all integers. Power residue symbol, a generalization of the Jacobi symbol to higher powers residues....

terms of a power residue symbol (p/q) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another...

the Legendre symbol is a function that can be used in formulas. It can also easily be generalized to cubic, quartic and higher power residues. There is a...

{\displaystyle \alpha ,\beta \in {\mathcal {O}}_{m},} the m-th power residue symbol for O m {\displaystyle {\mathcal {O}}_{m}} is either zero or an m-th...

quadratic residue modulo p; it is –1 if a is a quadratic non-residue modulo p; it is 0 if p divides a. The same notation is used for the Jacobi symbol and Kronecker...

The analogue of Legendre's original definition is used for higher-power residue symbols E.g. Kronecker's proof (Lemmermeyer, ex. p. 31, 1.34) is to use...

appear in Hilbert's reciprocity law for the power residue symbol. The definitions of the Hilbert symbol are usually rather roundabout and can be hard...

terms of a power residue symbol (p/q) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another...

n define the rational cubic residue symbol as [ m n ] 3 = { 1 m  is a cubic residue  mod n − 1 m  is a cubic non-residue  mod n {\displaystyle \left[{\frac...

least residue system is a complete residue system, and a complete residue system is simply a set containing precisely one representative of each residue class...

multiplication. The quadratic residue symbol in a Gauss sum is replaced by a higher residue symbol such as a cubic or quartic residue symbol, and the exponential...

Marc; Libert, Benoît (2017). "Efficient cryptosystems from 2k-th power residue symbols" (PDF). Journal of Cryptology. 30 (2): 519–549. doi:10.1007/s00145-016-9229-5...

Time Lords of Gallifrey. The symbol for the highest power level of a PSI attack in the Mother/EarthBound games A symbol used by U.S. citizens in the 1960s...

complex plane. Contour integration is closely related to the calculus of residues, a method of complex analysis. One use for contour integrals is the evaluation...

\pm 1{\pmod {p}}.} Define the rational quartic residue symbol for prime p ≡ 1 (mod 4) and quadratic residue a (mod p) as ( a p ) 4 = ± 1 ≡ a p − 1 4 ( mod...

rendering support, you may see question marks, boxes, or other symbols instead of APL symbols. The programming language APL is distinctive in being symbolic...

{e}}t}}^{n}(k,\mu _{\ell }^{\otimes n}).} This map is called the Galois symbol or norm residue map. Because étale cohomology with mod-ℓ coefficients is an ℓ-torsion...

component K2(F)m. It follows that every weakly continuous symbol factors through the norm residue symbol. Steinberg group (K-theory) Serre, Jean-Pierre (1996)...

R a power of two are faster than the available alternatives. Let N denote a positive integer modulus. The quotient ring Z/NZ consists of residue classes...

in f {\displaystyle f} is of particular interest; it is called formal residue of f {\displaystyle f} and denoted Res ⁡ ( f ) {\displaystyle \operatorname...

the ring of formal power series Fq[[T]]. Its maximal ideal is (T) (i.e. the power series whose constant term is zero) and its residue field is Fq. Its normalized...

a quadratic non-residue modulo p (this is almost the definition of a quadratic non-residue). There are p − 1/2 quadratic non-residues modulo p. For example...

(diatomite), carbon, non-volatile residues, lint, dyes, grease, soils, and water. The waste sludge or solid residue from the still contains residual solvent...

L-Tyrosine or tyrosine (symbol Tyr or Y) or 4-hydroxyphenylalanine is one of the 20 standard amino acids that are used by cells to synthesize proteins...